Rowling has said in an interview that the fact that Newt still has a wand after being expelled is 'significant'.
So Why did he get expelled?
J.K. Rowling: Well, he took the blame for something someone else did. That's significant, but I can't tell you why.
How did he keep a wand?
J.K. Rowling: How did he keep a wand? That's also significant, and I can't tell you why.